Mathematical Sciences: Interacting Particle Systems

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The project consists of four topics. The first deals with the approximation of the infinite particle systems by large finite systems as both the time and the size of the system tend to infinity. These results are particularly important from the point of view of the infinite particle systems as models for various practical problems. The second topic concerns the large deviation rate in a Poisson system of noninteracting random walks. The third topic can be described as the spread of the surviving particles following branching process models. The corresponding theoretical questions explore the clustering and coalescing behavior of the branching random walks. The last area of inquiry is relatively unexplored as yet. Multitype systems with non-attractive, non-additive state space, without duals arise naturally in epidemics or chemical reactions. Such systems are expected to exhibit new and interesting phenomena.